Nonlinear Mathematical Models of Metamaterials Defined as “Mass-in-Mass” and “Damper-in-Mass” Chains

D.A Kolesov

doi:10.21741/9781644901755-65

Abstract

Abstract. To describe dynamic processes in an acoustic (mechanical) metamaterial, there are proposed models that are a one-dimensional chain containing the same masses connected by linearly elastic (or nonlinearly elastic) elements (springs) with the same stiffness. In this case, it is assumed that each mass contains inside itself a series connection of another mass and an elastic element or viscous element (damper).

Highlights

An adequate description of the physical and mechanical properties of metamaterials within the framework of the classical theory of elasticity is impossible
Nonlinear elastic “mass-in-mass” chain In [3], to describe the dynamic properties of a metamaterial, a one-dimensional chain was considered containing the same masses mm1 connected by elastic elements with the same stiffness kk1, while each mass inside itself contained another mass mm2 and one more elastic element - a spring with stiffness kk2 (Fig. 1)
Let us generalize the model [3] by taking into account the quadratic nonlinearity of the external and internal elastic elements

Summary

Introduction

An adequate description of the physical and mechanical properties of metamaterials within the framework of the classical theory of elasticity is impossible. Nonlinear elastic “mass-in-mass” chain In [3], to describe the dynamic properties of a metamaterial, a one-dimensional chain was considered containing the same masses mm1 connected by elastic elements (springs) with the same stiffness kk1, while each mass inside itself contained another mass mm2 and one more elastic element - a spring with stiffness kk2 (Fig. 1). Let us generalize the model [3] by taking into account the quadratic nonlinearity of the external and internal elastic elements.

Results

Conclusion